Читать книгу Magnetic Resonance Microscopy - Группа авторов - Страница 41

After designing the dielectric resonator to operate under a given resonant mode (TE_01δ or HEM_11δ) for the required B0 field strength and sample dimensions and properties, the ceramic material fitting the electromagnetic properties found for the resonator must be chosen. Ferroelectric materials based on oxide titanites are adequate since the final permittivity and loss tangent are adjusted through the relative proportions of each constituent [11].

To properly excite a resonant mode, the excitation source must induce an electromagnetic field that overlaps with that of the mode, as illustrated in Figure 2.10: the excitation source is in this case equivalent to a magnetic dipole, and its position is chosen so that it is parallel to the magnetic polarization of the desired mode.

Figure 2.10 Example of excitation source: an electric current loop (magnetic dipole). Position required to excite the TE_01δ (left) and HEM_11δ (right) modes. The magnetic field lines (schematic) of each mode are represented. The static field direction is given by a thin arrow.

Regarding the first TE mode, analogous (in terms of field distribution) to a magnetic dipole parallel to the disk or ring axis, it is practical to use a small circular loop feed that is nonresonant at the Larmor frequency. This loop is positioned above the ceramic ring, with its axis parallel to that of the ring. In this configuration, the circulating current flowing through the loop creates an electric field distribution with the same cylindrical symmetry as that of the TE_01δ mode and therefore excites this mode. Higher-order modes with the same symmetry may be excited as well at their respective frequencies. Based on [29], in the case of small loops, we can maximize the quality factor of the whole probe (loop and dielectric resonator) by optimizing the distance between the loop and the resonator, or by changing the loop diameter at a given position.

In Figure 2.11, the influence of the loop position on the resonance is investigated with numerical simulations (CST Studio, Frequency Domain Solver), in the case of a disk whose first TE mode is located at 732 MHz (Eigenmode Solver of CST Studio). It was first checked that the excited mode was the TE_01δ mode: the magnetic field longitudinal component coincides in each configuration with the total magnetic field amplitude along the disk symmetry axis. As can be observed in Figure 2.11, the resonance frequency is slightly increased by the loop. The left column of Figure 2.11 shows that the maximum magnetic field at the center of the disk coincides with the minimum loop reflection coefficient, meaning the input power of the loop is transferred to the resonant mode of the disk. Also, but not shown in this figure, there exists an optimal loop diameter maximizing the magnetic field amplitude.

Figure 2.11 Influence on (left) the reflection coefficient S₁₁ (minimum value), the magnetic field amplitude (maximum value) at the center of the resonator, and (right) the corresponding frequency of the feeding loop position relative to the dielectric disk (relative permittivity 530, loss tangent 8.10⁻⁴, diameter 18 mm, height 10 mm). (a) Varying lateral position. (b) Varying longitudinal position. There is an optimal position of the feeding loop with a minimum reflection coefficient, and a maximum transmitted power to the resonant mode.

In the model proposed above (Section 2.3) for estimating the contribution of the ceramic probe to the SNR, the contribution of the feeding loop is neglected. In fact, this contribution depends on the loop’s geometry and material. For the geometry in Figure 2.11 and the considered probe prototype, the probe efficiency was compared for a lossy copper loop and an ideal loop in a perfect electric conductor; the difference was less than 0.2% between the two values.

The first hybrid mode can be excited as well by the same loop positioned on its lateral side. Another potential excitation source is an electric dipole antenna, generating a circulating magnetic field around the dipole axis and positioned on the lateral side of the resonator, perpendicular to the ring axis to excite the first TE mode, and parallel for the first hybrid electromagnetic (HEM) mode.

Figure 2.12 shows an example of an experimental setup exploiting a ceramic probe operating under its TE_01δ mode. In this setup, we use a circulating water blanket as a thermostat to homogenize and set the temperature of the ceramic probe at a given level. As depicted in Figure 2.13, the permittivity of the ceramic material and, as a result, the mode frequency, depend on its temperature, since reaching such a high permittivity value is enabled by working close to the Curie point of the ferroelectric material [7]. In [30], this dependence is used for real-time, accurate tuning of the probe to the Larmor frequency. However, in any other setup involving ceramic probes, even if another method is used for tuning, the temperature should be controlled to avoid the resonant frequency shifting away from the Larmor frequency.

Figure 2.12 Experimental setup. Fixing the resonant frequency at the Larmor frequency is enabled by thermostating the resonator at a given temperature (left). Matching is performed by sliding the excitation loop (right). With permission from [30].

Figure 2.13 Temperature dependence of the ceramic relative permittivity and therefore of the probe resonant frequency. With permission from [30].